Abstract

The total angular momentum per unit length of a general non-paraxial beam is decomposed into an orbital component associated with the spiral spectrum at the far field and a component concerning the balance between right- and left-handed circular-polarization content of the angular spectrum. Expressions for the linear momentum and energy per unit length are also provided. The well-known division into orbital and spin components is shown to be recovered in the paraxial limit.

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References

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
    [CrossRef] [PubMed]
  2. L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
    [CrossRef]
  3. L. Allen, and M. J. Padgett, “Introduction to phase-structured electromagnetic waves,” in Structured Light and Applications, D. L. Andrews, ed. (Academic Press, Burlington, MA, 2008).
  4. G. Molina-Terriza, “Determination of the total angular momentum of a paraxial beam,” Phys. Rev. A 78(5), 0538191–0538195 (2008).
    [CrossRef]
  5. S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110(5-6), 670–678 (1994).
    [CrossRef]
  6. G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: Preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 0136011–0136014 (2002).
  7. M. V. Vasnetsov, J. P. Torres, D. V. Petrov, and L. Torner, “Observation of the orbital angular momentum spectrum of a light beam,” Opt. Lett. 28(23), 2285–2287 (2003).
    [CrossRef] [PubMed]
  8. Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and ornital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281, 1968–1975 (2008).
  9. R. Martínez-Herrero and A. Manjavacas, “Overall second-order parametric characterization of light beams propagating through spiral phase elements,” Opt. Commun. 282(4), 473–477 (2009).
    [CrossRef]
  10. R. Martínez-Herrero, A. Manjavacas, and P. M. Mejías, “Cross-correlation between spiral modes and its influence on the overall spatial characteristics of partially coherent beams,” Opt. Express 17(22), 19857–19867 (2009).
    [CrossRef] [PubMed]
  11. R. Martínez-Herrero, P. M. Mejías, S. Bosch, and A. Carnicer, “Vectorial structure of nonparaxial electromagnetic beams,” J. Opt. Soc. Am. A 18(7), 1678–1680 (2001).
    [CrossRef]
  12. P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarizad laser beams,” Prog. Quantum Electron. 26(2), 65–130 (2002).
    [CrossRef]
  13. R. Martínez-Herrero, P. M. Mejías, S. Bosch, and A. Carnicer, “On the vectorial structure of nonparaxial radially polarized light fields,” Opt. Express 16, 9021–9033 (2008).
    [CrossRef] [PubMed]
  14. L. Torner, J. P. Torres, and S. Carrasco, “Digital spiral imaging,” Opt. Express 13(3), 873–881 (2005).
    [CrossRef] [PubMed]

2009

R. Martínez-Herrero and A. Manjavacas, “Overall second-order parametric characterization of light beams propagating through spiral phase elements,” Opt. Commun. 282(4), 473–477 (2009).
[CrossRef]

R. Martínez-Herrero, A. Manjavacas, and P. M. Mejías, “Cross-correlation between spiral modes and its influence on the overall spatial characteristics of partially coherent beams,” Opt. Express 17(22), 19857–19867 (2009).
[CrossRef] [PubMed]

2008

G. Molina-Terriza, “Determination of the total angular momentum of a paraxial beam,” Phys. Rev. A 78(5), 0538191–0538195 (2008).
[CrossRef]

Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and ornital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281, 1968–1975 (2008).

R. Martínez-Herrero, P. M. Mejías, S. Bosch, and A. Carnicer, “On the vectorial structure of nonparaxial radially polarized light fields,” Opt. Express 16, 9021–9033 (2008).
[CrossRef] [PubMed]

2005

2003

2002

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: Preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 0136011–0136014 (2002).

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarizad laser beams,” Prog. Quantum Electron. 26(2), 65–130 (2002).
[CrossRef]

2001

1999

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

1994

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110(5-6), 670–678 (1994).
[CrossRef]

1992

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Allen, L.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110(5-6), 670–678 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

Barnett, S. M.

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110(5-6), 670–678 (1994).
[CrossRef]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Bosch, S.

Carnicer, A.

Carrasco, S.

Gao, C.

Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and ornital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281, 1968–1975 (2008).

Gao, M.

Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and ornital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281, 1968–1975 (2008).

Li, F.

Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and ornital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281, 1968–1975 (2008).

Liu, Y.

Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and ornital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281, 1968–1975 (2008).

Manjavacas, A.

R. Martínez-Herrero, A. Manjavacas, and P. M. Mejías, “Cross-correlation between spiral modes and its influence on the overall spatial characteristics of partially coherent beams,” Opt. Express 17(22), 19857–19867 (2009).
[CrossRef] [PubMed]

R. Martínez-Herrero and A. Manjavacas, “Overall second-order parametric characterization of light beams propagating through spiral phase elements,” Opt. Commun. 282(4), 473–477 (2009).
[CrossRef]

Martínez-Herrero, R.

Mejías, P. M.

Molina-Terriza, G.

G. Molina-Terriza, “Determination of the total angular momentum of a paraxial beam,” Phys. Rev. A 78(5), 0538191–0538195 (2008).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: Preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 0136011–0136014 (2002).

Movilla, J. M.

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarizad laser beams,” Prog. Quantum Electron. 26(2), 65–130 (2002).
[CrossRef]

Padgett, M. J.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

Petrov, D. V.

Piquero, G.

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarizad laser beams,” Prog. Quantum Electron. 26(2), 65–130 (2002).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Torner, L.

L. Torner, J. P. Torres, and S. Carrasco, “Digital spiral imaging,” Opt. Express 13(3), 873–881 (2005).
[CrossRef] [PubMed]

M. V. Vasnetsov, J. P. Torres, D. V. Petrov, and L. Torner, “Observation of the orbital angular momentum spectrum of a light beam,” Opt. Lett. 28(23), 2285–2287 (2003).
[CrossRef] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: Preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 0136011–0136014 (2002).

Torres, J. P.

L. Torner, J. P. Torres, and S. Carrasco, “Digital spiral imaging,” Opt. Express 13(3), 873–881 (2005).
[CrossRef] [PubMed]

M. V. Vasnetsov, J. P. Torres, D. V. Petrov, and L. Torner, “Observation of the orbital angular momentum spectrum of a light beam,” Opt. Lett. 28(23), 2285–2287 (2003).
[CrossRef] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: Preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 0136011–0136014 (2002).

Vasnetsov, M. V.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Opt. Commun.

Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and ornital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281, 1968–1975 (2008).

R. Martínez-Herrero and A. Manjavacas, “Overall second-order parametric characterization of light beams propagating through spiral phase elements,” Opt. Commun. 282(4), 473–477 (2009).
[CrossRef]

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110(5-6), 670–678 (1994).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

G. Molina-Terriza, “Determination of the total angular momentum of a paraxial beam,” Phys. Rev. A 78(5), 0538191–0538195 (2008).
[CrossRef]

Phys. Rev. Lett.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: Preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 0136011–0136014 (2002).

Prog. Opt.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

Prog. Quantum Electron.

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarizad laser beams,” Prog. Quantum Electron. 26(2), 65–130 (2002).
[CrossRef]

Other

L. Allen, and M. J. Padgett, “Introduction to phase-structured electromagnetic waves,” in Structured Light and Applications, D. L. Andrews, ed. (Academic Press, Burlington, MA, 2008).

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Equations (6)

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rot B + i k E = 0 ,
rot E i k B = 0 ,
div E = 0 ,
div B = 0 ,
U = 1 16 π ( | E | 2 + | B | 2 ) d x d y ,
J z U = 1 ω m = + m 0 1 [ | f m ( ρ ) | 2 + | g m ( ρ ) | 2 ] ρ d ρ m = + 0 1 [ | f m ( ρ ) | 2 + | g m ( ρ ) | 2 ] ρ d ρ + + 1 ω m = + 0 1 [ | f m ( ρ ) | 2 | g m ( ρ ) | 2 ] ( ρ 2 2 1 ρ 2 + 1 ) ρ d ρ m = + 0 1 [ | f m ( ρ ) | 2 + | g m ( ρ ) | 2 ] ρ d ρ ,

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